In this parer, we mainly discuss the application of particle swarm optimization in the function optimization, which is one of swarm intelligent algorithms, and how to improve its performance. It is only several years since particle swarm optimization based on swarm behavior has been put forward,which originates from studying swarm behavior of the birds. Particle swarm optimization is simple,easily achieved and only need to adjust to very a few parameters.But it is impossible that particle swarm optimization can be used to solve any problems, that is to say, we need to improve or modify this algorithm when using it to solve concrete problems.We mainly research the defects of particle swarm optimization used in the optimization of non-constrained problems and constrained problems and put forward some relevant strategies according to the defects. At last, we apply the modified algorithm to the optimal design of thermal insulation on the pipeline.We have finished some research work in three respects as follows:Firstly, the optimization of non-constrained but multimodal functions with high-dimension. how to improve performance of particle swarm optimaziton when using it to handle this problem, which is low convergence speed and sensitivity to local convergence.This paper proposes an effective hybrid optimization strategy based on chaos optimization. Numerical simulation results on benchmark complex functions with high dimension show that the hybrid particle swarm optimaziton is effective and correct.Secondly, the optimization of constrained problems. how to handle this problem by using particle swarm optimization. In this paper, we use two different strategies .One is particle swarm optimization with penalty function.Owing to sensitive to local convergence of this method,we propose a strategy, which is degenerated mutation based on the variance of the population's fitness.The other is particle swarm optimization with double fitnesses. Some features of particle swarm optimization and a large number of constrained optimal problems are taken into account and then a new method is proposed, which means to separate the objective functions from its constrained functions. Therefore, every particle of particle swarm optimization has double fitness values. Numerical results show that the particle swarm optimization with double fitnesses is feasible and can get more precise results than particle swarm optimization with penalty functions and other optimization algorithms.Lastly, how to solve the optimal design of thermal insulation on the pipeline by using particle swarm optimization. It is the key to build the correctly mathematic modeling ,so at first we build the mathematic modeling of the optimal design of thermal insulation on the pipeline,then solve an actual example by using particle swarm optimization with double fitnesses.Numerical results show that this algrithm is feasible and can get more precise results than other methods . |